The party, which gained two seats in the election to hold 10 altogether, has not yet outlined what it might want from a formal deal with the Tories, but the prime minister said in her speech outside Downing Street that she could rely on her "friends and allies" from the DUP. She made the election about her and Jeremy Corbyn, but the electorate has largely said up yours to that sentiment.
"From hubris to humiliation", said the left-leaning Guardian. May has said her government will go ahead with these discussions as planned.
A party spokesperson confirmed the resignation of Hill, a combative character who one ex-colleague said had helped create a "toxic" atmosphere at the heart of government.
Corbyn's leadership refashioned the party, making it more about democratic socialism, pushing redistributive policies to deal with rampant inequalities, taxing the most-wealthy few to benefit the many.
Ms Foster has refused to resign over a scandal from her time as finance minister when it was found she had personally campaigned to keep a government-backed renewable-energy scheme opened despite it overspending by £400m (€455m).
I think, you know, we see this election extremely effective Labour Party campaign, which has not allowed the Labour Party to win the election outright but has enabled it to deny the conservatives and Prime Minister May a parliamentary majority.
Indeed, the prospect of a "hard" Brexit, by which the United Kingdom leaves with no deal, has shrunk with the Conservative majority, as it's a likely "red line" for the Democratic Unionist Party, the Northern Irish lawmakers May has turned to for support in Westminster.
The Protestant unionist party also had links with outlawed paramilitary groups during the years of Northern Ireland's "Troubles".
While the DUP campaigned to leave the European Union in last year's referendum, it has refused to endorse Mrs May's position that "no deal is better than a bad deal" - insisting that there must be no return of the "hard border" with the Republic.
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It was suspended in January when Sinn Fein withdrew from the agreement and said it would refuse to work with the DUP while First Minister Arlene Foster remained in her post.
European Council President Donald Tusk has warned there was "no time to lose" in starting talks, after May started the two-year countdown to Brexit on March 29.
Davidson, who led her party to its best result for three decades, winning 13 seats in Scotland, said she had sought and received assurances from May on the issue.
"One of them is country, one of the others is LGBTI rights".
He has been subjected to constant criticism along these lines, his leadership qualities, his political affiliations and his dress sense all routinely scrutinised and pilloried by politicians and by Britain's predominantly right-wing press.
MINORITY GOVERNMENT May had called the snap election with a view to increasing the narrow majority she had inherited from her predecessor David Cameron.
The Labour party, along with Momentum, the grassroots organisation of Corbyn supporters, galvanised the party's 500,000 strong members into taking to the streets, the phones and the internet to campaign for Labour.
Corbyn was given a major boost Sunday when a new poll by Survation gave Labour a five-point lead over the Conservatives following what has been universally described as a disastrous general election for May.
But Soubry said May's time in the top job would be limited.
May's weakened position in the party ruled out big changes.